How do I select a set of Blender elements with a common characteristic?
For a mesh in edit mode with 


vertex selection see the menu Select Similar.
face selection see the menu Select Similar Area
edge selection menu Select Similar Length 
Many other options




Circle Select with the Letter C Selects a circular distance in 2D in many, not all, cases.
To select a ring, first select objects by radius A, then second scroll mouse wheel to smaller radius B, then press Middle Mouse to button to remove the middle.  A minus B (A - B)

Still in mesh edit mode, if you are making a selection repeatedly, consider creating a vertex group for that selection.

Suggestion.  For Objects only.  If you are making the same selection many times. Consider Grouping those objects and thus select group.  Or more drastically create a common parent and select children.